Given that $16 xx 36=576$ , then find $sqrt(576)$ without a calculator using properties of perfect squares?

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Answer 1 · 2017-09-23T18:15:29

$sqrt(576) = 24$

Given:

$16 xx 36 = 576$

Then we can manipulate the LHS, noting that both $16$ and $36$ are perfect squares to get:

$16 xx 36 = 576$

$:. 4 xx 4 xx 6 xx 6 = 576$

$:. (4 xx 6) xx (4 xx 6) = 576$

$:. (4 xx 6)^2 = 576$

$:. (24)^2 = 576$

Hence:

$sqrt(576) = 24$

Given that 16 xx 36=57616 xx 36=576, then find sqrt(576)sqrt(576) without a calculator using properties of perfect squares?